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ehrenfest
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[SOLVED] group theory problem
Classify the factor group (Z_4 cross Z_4 cross Z_8)/<(1,2,4)> according to the fundamental theorem of finitely generated abelian groups.
<(1,2,4)> has order 4 so the factor group has order 32, so there are seven possibilities:
(Z_2)^5
Z_32
(Z_2)^3 cross Z_4
Z_16 cross Z_2
Z_8 cross Z_2 cross Z_2
Z_2 cross Z_4 cross Z_4
Z_8 cross Z_4
Anyone have any ideas about how to do this without doing a lot of tedious calculations?
Homework Statement
Classify the factor group (Z_4 cross Z_4 cross Z_8)/<(1,2,4)> according to the fundamental theorem of finitely generated abelian groups.
Homework Equations
The Attempt at a Solution
<(1,2,4)> has order 4 so the factor group has order 32, so there are seven possibilities:
(Z_2)^5
Z_32
(Z_2)^3 cross Z_4
Z_16 cross Z_2
Z_8 cross Z_2 cross Z_2
Z_2 cross Z_4 cross Z_4
Z_8 cross Z_4
Anyone have any ideas about how to do this without doing a lot of tedious calculations?